Question

a free-falling object increases speed by a little over 22 miles per hour each second. The arithmetic sequence 22 44 66 ...., represents speed after each second, in miles per hour of a dropped object. How fast is a rock falling after 8 seconds if it is dropped over the side of the cliff?

Answer 1

176 mph after 8 seconds

Explanation:

This is an arithmetic sequence with common difference 22 mph and first term 22. Thus, the nth term is a(n) = 22 + 22(n - 1).

Thus, the 8th term is a(8) = 22 + 22(7) = 176 mph

Answer 2

176 miles per hour

Explanation:

Givens

• The object increases speed by 22 miles per hour each second.
• The arithmetic sequence is 22, 44, 66, ...

After 8 seconds refers to the term number eight in the sequence, where the increasing difference is 22 miles per hour. So, the sequence until the second 8 is

`22mi/hr, 44mi/hr, 66mi/hr, 88mi/hr, 110mi/hr, 132 mi/hr, 154mi/hr, 176mi/hr`

Therefore, in the second number 8, the speed is 176 miles per hour, becuase it increases 22 miles per hour each second.